Hi Zelda -- Welcome to the forum! glad you found us! I took the liberty of moving your introductory post to the compost forum, since that's what your questions were about. We've got a number of regulars here who are really expert on compost; wanted to be sure they saw your questions. I'll make a start and then I expect some others will chime in.
Get something built! I can't imagine you can keep kitchen scraps in paper bags for very long, the bags do start breaking down. Which is a clue that yes you can put your bags in the compost pile. Do read the sticky at the top of this forum on greens and browns. The bags are a good brown for the pile.
How you get the compost out, depends on what kind of bin you have. The ones that look basically something like this:
[url=https://www.target.com/gp/detail.html/178-2784919-4221865?ASIN=B001D4OS0U&AFID=Froogle&LNM=B001D4OS0U%7CGarden_Compost_Bin&ci_src=14110944&ci_sku=B001D4OS0U&ref=tgt_adv_XSG10001]Garden Compost Bin[/url]
usually have a door at the bottom. After a few months you can just pull finished compost out from the bottom.
The tumbler varieties are basically batch composters. You load it up with the stuff you've been saving up, tumble it for a few weeks (so they say, I've never tried one) until the compost is finished and then dump the whole thing out and start over.
What you do with it is mix it in to your soil. If you are tilling up a new bed spread it out and till it in. If you are planting put some in your planting hole and trowel it in a bit. If everything is planted already, just spread some on top of the ground for mulch and trowel it in a bit. But unless you have a tumbler, what to do with your compost isn't going to be your problem until spring.
If you have a regular bin like the picture and it sits on the ground, you don't have to buy worms, they will come. If you have a tumbler or something else that doesn't touch the ground it would be good to throw a few handfuls of soil in with the other compostables. If you can find a couple earthworms while you are digging up soil that would be good. Or it would be a good chance to meet some neighbors: Hi I'm your new next door neighbor, can I borrow a cup of earthworms!
Your bush doesn't go in the compost pile unless you can run it through a chipper/shredder first, but you can start a separate brush pile and it will break down over a period of years. In the meantime it makes nice critter habitat. I also use my brush pile as a source of kindling for the fire pit... a firepit makes a wonderful addition to a garden and they are pretty cheap these days. Haven't used mine much this year, because it's been raining all the time and even if it stops for a minute, everything burnable is so soaked... Anyway, woops I got off the topic of compost!
I don't think dryer sheets are compostable, they are impregnated with chemicals.
What you have gotten yourself into is a wonderful hobby that will bring you joy for years to come, while helping turn your little neglected piece of earth into a beautiful living biosphere. Once you have the results of seeing your kitchen scraps and weeds turn into rich dark earth and then flowers and veggies, I believe you will be hooked, like the rest of us here!